Electric field distribution and energy absorption in anisotropic and dispersive red blood cells

Electrochemical Impedance Characterization of Blood Cell Suspensions. Part 1: Basic Theory and Application to Two-Phase Systems

Electrochemical impedance spectra of composite materials contain information on the topological arrangement, volume fraction, and shape of particles, as well as the dielectric properties of the matrix and particles. The objective of this study is to investigate how these parameters affect the dielectric spectrum and what reliable information can be extracted from experimental data. The main attention was focused on systems with dielectric behavior similar to that of human blood. Mostly plasma and erythrocytes determine the dielectric properties of whole blood. Erythrocytes suspended in plasma can be considered as three-phase systems with single-shelled particles. A theoretical approach based on the effective medium theory is developed for calculating the effective permittivity and conductivity of three-phase composites at a wide frequency range (from 0 to 1 GHz). A finite-difference method is applied to model three-dimensional periodic structures. A special case of two-phase materials is used to demonstrate the influence of the shape and arrangement of particles on dielectric properties. Theoretical and numerical approaches are applied to two-phase composites with spherical, spheroidal and biconcave particles and are compared with each other and with published data. It is shown that two-phase composites exhibit only β-dispersion. In contrast to the quasi-static limit, the wide-bandwidth impedance spectroscopy makes it possible to distinguish between disordered and regular arrangements of spheroidal and biconcave particles. The results can be used to analyze the dielectric properties of blood, which is very promising for various medical applications. This study of two-phase composites can be further extended to three-phase composites.

Treatment planning with intensity modulated particle therapy for multiple targets in stage IV non-small cell lung cancer

Intensity modulated particle therapy (IMPT) can produce highly conformal plans, but is limited in advanced lung cancer patients with multiple lesions due to motion and planning complexity. A 4D IMPT optimization including all motion states was expanded to include multiple targets, where each target (isocenter) is designated to specific field(s). Furthermore, to achieve stereotactic treatment planning objectives, target and OAR weights plus objective doses were automatically iteratively adapted. Finally, 4D doses were calculated for different motion scenarios. The results from our algorithm were compared to clinical stereotactic body radiation treatment (SBRT) plans. The study included eight patients with 24 lesions in total. Intended dose regimen for SBRT was 24 Gy in one fraction, but lower fractionated doses had to be delivered in three cases due to OAR constraints or failed plan quality assurance. The resulting IMPT treatment plans had no significant difference in target coverage compared to SBRT treatment plans. Average maximum point dose and dose to specific volume in OARs were on average 65% and 22% smaller with IMPT. IMPT could also deliver 24 Gy in one fraction in a patient where SBRT was limited due to the OAR vicinity. The developed algorithm shows the potential of IMPT in treatment of multiple moving targets in a complex geometry.

Intracellular potassium under osmotic stress determines the dielectrophoresis cross-over frequency of murine myeloma cells in the MHz range

Dielectrophoresis (DEP) has been widely studied for its potential as a biomarker-free method of sorting and characterizing cells based upon their dielectric properties. Most studies have employed voltage signals from ∼1 kHz to no higher than ∼30 MHz. Within this range a transition from negative to positive DEP can be observed at the cross-over frequency f_x01 . The value of f_x01 is determined by the conductivity of the suspending medium, as well as the size and shape of the cell and the dielectric properties (capacitance, conductivity) of its plasma membrane. In this work DEP measurements were performed up to 400 MHz, where the transition from positive to negative DEP can be observed at a higher cross-over frequency f_x02 . SP2/O murine myeloma cells were suspended in buffer media of different osmolarities and measurements taken of cell volume, f_x01 and f_x02 . Potassium-binding benzofuran isophthalate (PBFI), a potassium-sensitive fluorophore, and flow cytometry was employed to monitor relative changes in intracellular potassium concentration. In agreement with theory, it was found that f_x02 is independent of the cell parameters that control f_x01 and is predominantly determined by intracellular conductivity. In particular, the value of f_x02 is highly correlated to that of the intracellular potassium concentration.

Towards a realistic dielectric tissue model: a multiscale approach

In the past, mainly analytical mixing formulas were used for modeling of dielectric properties of biological cells. General drawbacks of such formulas are the restriction to simple shapes and small cellular volume fractions. Assuming cell suspensions or tissues being quasi-periodic the problem size can be reduced to a cubic unit cell containing a single biological cell. Under this assumption numerical, e.g. Finite- Element models of such unit cells provide effective dielectric parameters for the entire tissue or cell suspension. In this work a flexible shape parametrization method allowing for a realistic representation of biological cells is applied to eight different cell types. A non-axisymmetric columnar epithelium cell occurring e.g. in the epidermis is chosen as an example. Numerical simulations of the columnar cell exposed to a time-harmonic electric field are performed for two different, high volume fractions, followed by the extraction of effective dielectric parameters of the bulk material. The simulation results are compared to two analytical approximations for ellipsoidal particles. The results suggest, that the calculation of effective dielectric properties of arbitrarily shaped cells in the frequency range between 100kHz and 1GHz requires at least a numerical cell model.

Validation of human skin models in the MHz region

The human skin consists of several layers with distinct dielectric properties. Resolving the impact of changes in dielectric parameters of skin layers and predicting them allows for non-invasive sensing in medical diagnosis. So far no complete skin and underlying tissue model is available for this purpose in the MHz range. Focusing on this dispersiondominated frequency region multilayer skin models are investigated: First, containing homogeneous non-dispersive sublayers and second, with sublayers obtained from a three-phase Maxwell-Garnett mixture of shelled cell-like ellipsoids. Both models are numerically simulated using the Finite Element Method, a fringing field sensor on the top of the multilayer system serving as a probe. Furthermore, measurements with the sensor probing skin in vivo are performed. In order to validate the models the uppermost skin layer, the stratum corneum was i) included and ii) removed in models and measurements. It is found that only the Maxwell-Garnett mixture model can qualitatively reproduce the measured dispersion which still occurs without the stratum corneum and consequently, structural features of tissue have to be part of the model.

Polarizability of shelled particles of arbitrary shape in lossy media with an application to hematic cells

We show that within the dipole approximation the complex polarizability of shelled particles of arbitrary shape can be written as the volume of the particle times a weighted average of the electric field in the particle, with weights determined by the differences in permittivities between the shells and the external, possibly lossy media. To calculate the electric field we use an adaptive-mesh finite-element method which is very effective in handling the irregular domains, material inhomogeneities, and complex boundary conditions usually found in biophysical applications. After extensive tests with exactly solvable models, we apply the method to four types of hematic cells: platelets, T-lymphocytes, erythrocytes, and stomatocytes. Realistic shapes of erythrocytes and stomatocytes are generated by a parametrization in terms of Jacobi elliptic functions. Our results show, for example, that if the average polarizability is the main concern, a confocal ellipsoid may be used as a model for a normal erythrocyte, but not for a stomatocyte. A comparison with experimental electrorotation data shows quantitatively the effect of an accurate geometry in the derivation of electrical cell parameters from fittings of theoretical models to the experimental data.